Next Article in Journal
The Symmetric-Partitioning and Incremental-Relearning Classification and Back-Propagation-Network Tree Approach for Cycle Time Estimation in Wafer Fabrication
Next Article in Special Issue
Wigner’s Space-Time Symmetries Based on the Two-by-Two Matrices of the Damped Harmonic Oscillators and the Poincaré Sphere
Previous Article in Journal
Hydrodynamic Helical Orientations of Nanofibers in a Vortex
Previous Article in Special Issue
Closed-Form Expressions for the Matrix Exponential
Symmetry 2014, 6(2), 396-408; doi:10.3390/sym6020396
Article

Invisibility and PT Symmetry: A Simple Geometrical Viewpoint

*  and
Received: 24 February 2014 / Revised: 12 May 2014 / Accepted: 14 May 2014 / Published: 22 May 2014
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
View Full-Text   |   Download PDF [258 KB, uploaded 22 May 2014]

Abstract

We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via Möbius transformations, as parallel displacements, a geometric action that has no Euclidean analogy.
Keywords: ΡT symmetry; SL(2, C); Lorentz group; Hyperbolic geometry ΡT symmetry; SL(2, C); Lorentz group; Hyperbolic geometry
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Share & Cite This Article

Further Mendeley | CiteULike
Export to BibTeX |
EndNote
MDPI and ACS Style

Sánchez-Soto, L.L.; Monzón, J.J. Invisibility and PT Symmetry: A Simple Geometrical Viewpoint. Symmetry 2014, 6, 396-408.

View more citation formats

Article Metrics

For more information on the journal, click here

Comments

Cited By

[Return to top]
Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert